A probabilistic string is a sequence of probability vectors. Each vector specifies a probability distribution over the possible symbols at its location in the string. In a probabilistic grammar a probability is assigned to every derivation. Given a probabilistic string and a probabilistic grammar the concept of a maximal derivation is defined. Algorithms for finding the maximal derivation for p...

For a $d$-dimensional random vector $X$, let $p_{n, X}(\theta)$ be the probability that convex hull of $n$ independent copies $X$ contains given point $\theta$. We provide several sharp inequalities regarding and $N_X(\theta)$ denoting smallest for which X}(\theta)\ge1/2$. As main result, we derive totally general inequality $1/2 \le \alpha_X(\theta)N_X(\theta)\le 3d + 1$, where $\alpha_X(\thet...

Sentiment analysis is to extract the opinion of the user from of the text documents. Sentiment classification using machine learning methods face problem of handling huge number of unique terms in a feature vector for the classification. Thus it is required to eliminate the irrelevant and noisy terms from the feature vector. Feature selection methods reduce the feature size by selecting promine...

We start by stating a version of the Perron–Frobenius theorem. Let A be a d × d stochastic matrix, where here we use this to mean that the entries of A are non-negative, and every column sums to 1: Aij ∈ [0, 1] for all i, j, and ∑d i=1Aij = 1 for all j. Thus the columns of A are probability vectors. Such a matrix A describes a weighted random walk on d sites: if the walker is presently at site ...

We propose a universal ensemble for the random selection of rate–distortion codes which is asymptotically optimal in sample-wise sense. According to this ensemble, each reproduction vector, x^, selected independently at under probability distribution that proportional 2−LZ(x^), where LZ(x^) code length x^ pertaining 1978 version Lempel–Ziv (LZ) algorithm. show that, with high probability, resul...

A fundamental problem in the transmission of analog information across a noisy discrete channel is the choice of channel code rate that optimally allocates the available transmission rate between lossy source coding and block channel coding. We establish tight bounds on the channel code rate that minimizes the average distortion of a vector quantizer cascaded with a channel coder and a binary-s...

The aim of this paper is to revisit the problem of nonlinear channel equalization. The equalization is here viewed as the estimation, from the observation of the channel output, of the state vector of the channel consisting of the last transmitted symbols. If the probability density function of the state vector given all the available observations, (the a posteriori density function) were known...

In this paper, a new method is presented to estimate the 3D pose of facial image based on statistical Gaussian error models. The basic idea is that the pose angle can be computed by the orthogonal projection computation if the specific 3D shape vector of the given person is known. In our algorithm, Gaussian probability density function is used to model the distributions of the 3D shape vector a...

In this paper, we extend a type of Strassen’s theorem for the existence of probability measures with given marginals to positive vector measures with values in the dual of a barreled locally convex space which has certain order conditions. In this process of the extension we also give some useful properties for vector measures with values in dual spaces.

In this technical report, we will make two observations concerning symmetries of the probability distribution resulting from projection of a piece of p-dimensional data onto a random m-dimensional subspace of $\mathbb{R}^p$, where m<p. In particular, we shall observe that such distributions are unchanged by reflection across the original data vector and by rotation about the original data vector